diff options
| author | Camil Staps | 2016-03-23 22:48:31 +0100 |
|---|---|---|
| committer | Camil Staps | 2016-03-23 22:48:31 +0100 |
| commit | dc939bc8e5e2578b325f748537f4f8591e07be3e (patch) | |
| tree | e3d164368dd704e9fee5029e915f9e10b6e3a2bf /assignment8/qs.prf | |
| parent | Assignment 7 (diff) | |
Start assignment 8
Diffstat (limited to 'assignment8/qs.prf')
| -rw-r--r-- | assignment8/qs.prf | 1706 |
1 files changed, 1706 insertions, 0 deletions
diff --git a/assignment8/qs.prf b/assignment8/qs.prf new file mode 100644 index 0000000..1467ace --- /dev/null +++ b/assignment8/qs.prf @@ -0,0 +1,1706 @@ +(my_list_induction + (less_wf 0 + (less_wf-1 nil 3667405436 + ("" (expand "well_founded?") + (("" (skolem 1 P) + (("" (flatten) + (("" (skolem -1 Y) + (("" (expand "less") + (("" (lemma naturalnumbers.wf_nat) + (("" (expand "well_founded?") + (("" + (inst -1 "(LAMBDA(n:nat):EXISTS(l:(P)):length(l)=n)") + (("" (split) + (("1" (skosimp*) + (("1" (typepred y!1) + (("1" (skolem -1 L) + (("1" (inst 1 L) + (("1" (skolem 1 G) + (("1" + (inst -2 "length(G)") + (("1" (assert) nil nil) + ("2" + (typepred G) + (("2" (inst 1 G) nil nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil) + ("2" (grind) + (("2" (inst 1 "length(Y)") + (("2" (inst 1 Y) nil nil)) nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil) + ((well_founded? const-decl "bool" orders nil) + (less const-decl "bool" my_list_induction nil) + (NOT const-decl "[bool -> bool]" booleans nil) + (P skolem-const-decl "pred[list[X]]" my_list_induction nil) + (G skolem-const-decl "(P)" my_list_induction nil) + (real_lt_is_strict_total_order name-judgement + "(strict_total_order?[real])" real_props nil) + (length def-decl "nat" list_props nil) + (= const-decl "[T, T -> boolean]" equalities nil) + (list type-decl nil list_adt nil) + (X formal-type-decl nil my_list_induction nil) + (pred type-eq-decl nil defined_types nil) + (nat nonempty-type-eq-decl nil naturalnumbers nil) + (>= const-decl "bool" reals nil) + (bool nonempty-type-eq-decl nil booleans nil) + (int nonempty-type-eq-decl nil integers nil) + (integer_pred const-decl "[rational -> boolean]" integers nil) + (rational nonempty-type-from-decl nil rationals nil) + (rational_pred const-decl "[real -> boolean]" rationals nil) + (real nonempty-type-from-decl nil reals nil) + (real_pred const-decl "[number_field -> boolean]" reals nil) + (number_field nonempty-type-from-decl nil 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(number_field_pred const-decl "[number -> boolean]" number_fields + nil) + (number_field nonempty-type-from-decl nil number_fields nil) + (real_pred const-decl "[number_field -> boolean]" reals nil) + (real nonempty-type-from-decl nil reals nil) + (rational_pred const-decl "[real -> boolean]" rationals nil) + (rational nonempty-type-from-decl nil rationals nil) + (integer_pred const-decl "[rational -> boolean]" integers nil) + (int nonempty-type-eq-decl nil integers nil) + (bool nonempty-type-eq-decl nil booleans nil) + (>= const-decl "bool" reals nil) + (nat nonempty-type-eq-decl nil naturalnumbers nil) + (< const-decl "bool" reals nil) + (NOT const-decl "[bool -> bool]" booleans nil) + (occ def-decl "nat" my_list_props nil) + (> const-decl "bool" reals nil) (lwb const-decl "bool" SPLIT nil) + (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) + (AND const-decl "[bool, bool -> bool]" booleans nil) + (PRED type-eq-decl nil defined_types nil) + (list type-decl nil list_adt nil)) + nil)) + (upb_perm 0 + (upb_perm-1 nil 3658132945 + ("" (skosimp*) + (("" (lemma occ_upb) + (("" (inst? -1) + (("" (assert) + (("" (expand "upb") + (("" (skosimp*) + (("" (expand "perm?") + (("" (lemma nth_occ) + (("" (inst? -1) + (("" (assert) + (("" (inst? -3) + (("" (lemma occ_nth) + (("" (inst -1 l!1 "nth(lp!1, i!1)") + (("" (assert) + (("" + (skosimp*) + (("" + (inst? -4) + (("" (assert) nil nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil) + ((occ_upb formula-decl nil QS_props nil) + (nth_occ formula-decl nil my_list_props nil) + (real_lt_is_strict_total_order name-judgement + "(strict_total_order?[real])" real_props nil) + (occ_nth formula-decl nil my_list_props nil) + (real_gt_is_strict_total_order name-judgement + "(strict_total_order?[real])" real_props nil) + (< const-decl "bool" reals nil) + (length def-decl "nat" list_props nil) + (below type-eq-decl nil nat_types nil) + (nth def-decl "T" list_props nil) + (perm? const-decl "bool" my_list_props nil) + (upb const-decl "bool" SPLIT nil) + (AND const-decl "[bool, bool -> bool]" booleans nil) + (PRED type-eq-decl nil defined_types nil) + (list type-decl nil list_adt nil) + (nat nonempty-type-eq-decl nil naturalnumbers nil) + (>= const-decl "bool" reals nil) + (bool nonempty-type-eq-decl nil booleans nil) + (int nonempty-type-eq-decl nil integers nil) + (integer_pred const-decl "[rational -> boolean]" integers nil) + (rational nonempty-type-from-decl nil rationals nil) + (rational_pred const-decl "[real -> boolean]" rationals nil) + (real nonempty-type-from-decl nil reals nil) + (real_pred const-decl "[number_field -> boolean]" reals nil) + (number_field nonempty-type-from-decl nil number_fields nil) + (number_field_pred const-decl "[number -> boolean]" number_fields + nil) + (boolean nonempty-type-decl nil booleans nil) + (number nonempty-type-decl nil numbers nil)) + shostak)) + (lwb_perm 0 + (lwb_perm-1 nil 3658138209 + ("" (skosimp*) + (("" (lemma occ_lwb) + (("" (inst? -1) + (("" (assert) + (("" (expand "lwb") + (("" (skosimp*) + (("" (expand "perm?") + (("" (lemma nth_occ) + (("" (inst? -1) + (("" (assert) + (("" (inst? -3) + (("" (lemma occ_nth) + (("" (inst -1 l!1 "nth(lp!1, i!1)") + (("" (assert) + (("" + (skosimp*) + (("" + (inst? -4) + (("" (assert) nil nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil)) + nil) + ((occ_lwb formula-decl nil QS_props nil) + (nth_occ formula-decl nil my_list_props nil) + (real_lt_is_strict_total_order name-judgement + "(strict_total_order?[real])" real_props nil) + (occ_nth formula-decl nil my_list_props nil) + (real_gt_is_strict_total_order name-judgement + "(strict_total_order?[real])" real_props nil) + (< const-decl "bool" reals nil) + (length def-decl "nat" list_props nil) + (below type-eq-decl nil nat_types nil) + (nth def-decl "T" list_props nil) + (perm? const-decl "bool" my_list_props nil) + (lwb const-decl "bool" SPLIT nil) + (AND const-decl "[bool, bool -> bool]" booleans nil) + (PRED type-eq-decl nil defined_types nil) + (list type-decl nil list_adt nil) + (nat nonempty-type-eq-decl nil naturalnumbers nil) + (>= const-decl "bool" reals nil) + (bool nonempty-type-eq-decl nil booleans nil) + (int nonempty-type-eq-decl nil integers nil) + (integer_pred const-decl "[rational -> boolean]" integers nil) + (rational nonempty-type-from-decl nil rationals nil) + (rational_pred const-decl "[real -> boolean]" rationals nil) + (real nonempty-type-from-decl nil reals nil) + (real_pred const-decl "[number_field -> boolean]" reals nil) + (number_field nonempty-type-from-decl nil number_fields nil) + (number_field_pred const-decl "[number -> boolean]" number_fields + nil) + (boolean nonempty-type-decl nil booleans nil) + (number nonempty-type-decl nil numbers nil)) + nil)) + (qs_sorted 0 + (qs_sorted-1 nil 3658128963 + ("" (lemma list_length_induction) (("" (postpone) nil nil)) nil) + ((list type-decl nil list_adt nil) + (PRED type-eq-decl nil defined_types nil) + (AND const-decl "[bool, bool -> bool]" booleans nil) + (pred type-eq-decl nil defined_types nil) + (sorted? const-decl "bool" SORTED nil) + (qs def-decl "list[nat]" QS nil) + (split_lwb_upb formula-decl nil SPLIT nil) + (cdr adt-accessor-decl "[(cons?) -> list]" list_adt nil) + (car adt-accessor-decl "[(cons?) -> T]" list_adt nil) + (cons? adt-recognizer-decl "[list -> boolean]" list_adt nil) + (split_length formula-decl nil SPLIT nil) + (sorted_append formula-decl nil SORTED nil) + (lwb_perm formula-decl nil QS_props nil) + (qs_perm formula-decl nil QS_props nil) + (perm_commutative formula-decl nil my_list_props nil) + (nth def-decl "T" list_props nil) + (real_lt_is_strict_total_order name-judgement + "(strict_total_order?[real])" real_props nil) + (posint_plus_nnint_is_posint application-judgement "posint" + integers nil) + (real_le_is_total_order name-judgement "(total_order?[real])" + real_props nil) + (numfield nonempty-type-eq-decl nil number_fields nil) + (- const-decl "[numfield, numfield -> numfield]" number_fields nil) + (int_minus_int_is_int application-judgement "int" integers nil) + (real_ge_is_total_order name-judgement "(total_order?[real])" + real_props nil) + (lwb const-decl "bool" SPLIT nil) + (upb_perm formula-decl nil QS_props nil) + (less const-decl "bool" my_list_induction nil) + (split def-decl "[list[nat], list[nat]]" SPLIT nil) + (cons adt-constructor-decl "[[T, list] -> (cons?)]" list_adt nil) + (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" + integers nil) + (length def-decl "nat" list_props nil) + (list_length_induction formula-decl nil my_list_induction nil) + (number nonempty-type-decl nil numbers nil) + (boolean nonempty-type-decl nil booleans nil) + (number_field_pred const-decl "[number -> boolean]" number_fields + nil) + (number_field nonempty-type-from-decl nil number_fields nil) + (real_pred const-decl "[number_field -> boolean]" reals nil) + (real nonempty-type-from-decl nil reals nil) + (rational_pred const-decl "[real -> boolean]" rationals nil) + (rational nonempty-type-from-decl nil rationals nil) + (integer_pred const-decl "[rational -> boolean]" integers nil) + (int nonempty-type-eq-decl nil integers nil) + (bool nonempty-type-eq-decl nil booleans nil) + (>= const-decl "bool" reals nil) + (nat nonempty-type-eq-decl nil naturalnumbers nil)) + shostak))) + |